Physics-guided tabular prior-data fitted network distillation for prediction and optimisation of concrete-filled aluminium tube stub columns

Accurate prediction and optimisation of composite structural members are often constrained by limited experimental data, nonlinear material behaviour, and model uncertainty. This study proposes a residual-calibrated, physics-guided symbolic distillation framework for predicting and optimising the load-carrying capacity of concrete-filled aluminium tube stub columns. The framework integrates a Tabular Prior-Data Fitted Network, a transformer-based meta-learning model, with a synthetic data distillation pipeline and symbolic regression to enable interpretable modelling under small-data conditions. The framework integrates high-accuracy prediction, residual-calibrated prediction intervals, and symbolic interpretability within a single pipeline. Benchmarking against five machine learning models demonstrated the superior predictive performance of the proposed framework, which achieved a coefficient of determination of 99.53% on test data. Furthermore, a physics-guided symbolic equation was extracted and validated, achieving a coefficient of determination of 99.42%. The surrogate model is further embedded into a Non-dominated Sorting Genetic Algorithm II framework for multi-objective optimisation of cost and carbon footprint under structural constraints. Computational inverse-design optimisation across 29 held-out specimens yielded average unit-length reductions of 30.38% in material cost and 31.29% in carbon footprint, while maintaining load capacities within a 5% exceedance. However, the symbolic formulation is empirical and derived from a limited dataset, constraining extrapolation beyond the studied domain.